Reviewer:

In this contribution, the authors report an interesting study on the 
effects of the viscous correction to the widely used Cooper-Frye 
formulae. In particular the authors completed the particle spectra 
of identified hadrons and anisotropic flows (v2 and v3) which appear 
to compare well with experimental data. The paper shall be 
published, after the authors clarify two minor issues, as follows:

1) I am somewhat confused about the v2 and v3 results presented in 
Fig.2: are those obtained from the viscous Cooper-Frye in Eq.(10) or 
are they obtained from the more “naive” formula in Eq.(6)? The 
comments at the end seem to suggest that Eq.(6) is used, while one 
would have expected that the Eq.(10) shall provide a more serious 
calculation.

2) For the Eq.(12) — it goes without saying that such Bjorken 
scaling formula is merely a useful “guideline” estimate. It is well 
known that at late stage the transverse expansion becomes 
significant and the deviation from Bjorken flow becomes large. Just 
curious whether this info could be simply taken from some hydro 
simulations. Or at least some comments may be useful here regarding 
how good this approximation would be and what are the potential 
uncertainty brought in by it (e.g. compared with using a 3D Hubble 
formula).


Response:

We thank the referee for his constructive criticisms which has 
helped us to improve the presentation of the manuscript. In the 
following, we address the issues raised by the referee.

(1) In the previous version of the manuscript, the expression for 
$u_n$ from Eq. (6) is substituted in Eq. (1) to obtain the fluid 
velocity profile which is used in Eq. (10) to obtain $v_n$ as shown 
in Fig. 2. This is now clarified in the revised version of the 
manuscript after Eq. (5).

(2)  While the Bjorken estimate for the absolute values of the 
freeze-out times is rather crude, as pointed out by the referee, we 
have used the above equation to fix the freeze-out time for 
non-central collisions relative to that of the most central ones. In 
the present case, it seems to be a reliable approximation as is 
evident from Fig. 1. This is now explained in the revised manuscript 
after Eq. (11).

We believe that we have addressed the concerns of the referee and we 
sincerely hope that he finds the revised manuscript acceptable for 
publication.